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@ARTICLE{Burkhardt:890364,
      author       = {Burkhardt, T. W. and Eisenriegler, E.},
      title        = {{T}wo-dimensional critical systems with mixed boundary
                      conditions: {E}xact {I}sing results from conformal
                      invariance and boundary-operator expansions},
      journal      = {Physical review / E},
      volume       = {103},
      number       = {1},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2021-00909},
      pages        = {012120},
      year         = {2021},
      abstract     = {With conformal-invariance methods, Burkhardt, Guim, and Xue
                      studied the critical Ising model, defined on the upper half
                      plane y>0 with different boundary conditions a and b on the
                      negative and positive x axes. For ab=−+ and f+, they
                      determined the one- and two-point averages of the spin σ
                      and energy ε. Here +,−, and f stand for spin-up,
                      spin-down, and free-spin boundaries, respectively. The case
                      +−+−+⋯, where the boundary condition switches between
                      + and − at arbitrary points, ζ1,ζ2,⋯ on the x axis was
                      also analyzed. In the first half of this paper a similar
                      study is carried out for the alternating boundary condition
                      +f+f+⋯ and the case −f+ of three different boundary
                      conditions. Exact results for the one- and two-point
                      averages of σ,ε, and the stress tensor T are derived with
                      conformal-invariance methods. From the results for ⟨T⟩,
                      the critical Casimir interaction with the boundary of a
                      wedge-shaped inclusion is derived for mixed boundary
                      conditions. In the second half of the paper, arbitrary
                      two-dimensional critical systems with mixed boundary
                      conditions are analyzed with boundary-operator expansions.
                      Two distinct types of expansions—away from switching
                      points of the boundary condition and at switching
                      points—are considered. Using the expansions, we express
                      the asymptotic behavior of two-point averages near
                      boundaries in terms of one-point averages. We also consider
                      the strip geometry with mixed boundary conditions and derive
                      the distant-wall corrections to one-point averages near one
                      edge due to the other edge. Finally we confirm the
                      consistency of the predictions obtained with
                      conformal-invariance methods and with boundary-operator
                      expansions, in the the first and second halves of the
                      paper.},
      cin          = {IBI-5},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IBI-5-20200312},
      pnm          = {524 - Molecular and Cellular Information Processing
                      (POF4-524)},
      pid          = {G:(DE-HGF)POF4-524},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000608619900005},
      doi          = {10.1103/PhysRevE.103.012120},
      url          = {https://juser.fz-juelich.de/record/890364},
}